# log, logf, logl

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< c‎ | numeric‎ | math

Defined in header ``<math.h>`` |  |
float logf( float arg ); | (1) | (since C99)
double log( double arg ); | (2) |
long double logl( long double arg ); | (3) | (since C99)
Defined in header ``<tgmath.h>`` |  |
#define log( arg ) | (4) | (since C99)

1-3) Computes the natural (base e) logarithm of arg.
4) Type-generic macro: If arg has type long double, `logl` is called. Otherwise, if arg has integer type or the type double, `log` is called. Otherwise, `logf` is called. If arg is complex or imaginary, then the macro invokes the corresponding complex function (clogf, clog, clogl).

### Parameters

arg | - | floating-point value

### Return value

If no errors occur, the natural (base-e) logarithm of arg (ln(arg) or loge(arg)) is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a pole error occurs, -HUGE_VAL, `-HUGE_VALF`, or `-HUGE_VALL` is returned.

### Error handling

Errors are reported as specified in `math_errhandling`.

Domain error occurs if arg is less than zero.

Pole error may occur if arg is zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

- If the argument is ±0, -∞ is returned and FE_DIVBYZERO is raised.
- If the argument is 1, +0 is returned
- If the argument is negative, NaN is returned and FE_INVALID is raised.
- If the argument is +∞, +∞ is returned
- If the argument is NaN, NaN is returned.

### Example

Run this code

    #include <errno.h>
    #include <fenv.h>
    #include <float.h>
    #include <math.h>
    #include <stdio.h>
    // #pragma STDC FENV_ACCESS ON

    int main(void)
    {
        printf("log(1) = %f\n", log(1));
        printf("base-5 logarithm of 125 = %f\n", log(125) / log(5));

        // special values
        printf("log(1) = %f\n", log(1));
        printf("log(+Inf) = %f\n", log(INFINITY));

        // error handling
        errno = 0; feclearexcept(FE_ALL_EXCEPT);
        printf("log(0) = %f\n", log(0));
        if (errno == ERANGE)
            perror("    errno == ERANGE");
        if (fetestexcept(FE_DIVBYZERO))
            puts("    FE_DIVBYZERO raised");
    }

Output:

    log(1) = 0.000000
    base-5 logarithm of 125 = 3.000000
    log(1) = 0.000000
    log(+Inf) = inf
    log(0) = -inf
        errno == ERANGE: Numerical result out of range
        FE_DIVBYZERO raised

### References

- C23 standard (ISO/IEC 9899:2024):

  - 7.12.6.7 The log functions (p: TBD)

  - 7.25 Type-generic math <tgmath.h> (p: TBD)

  - F.10.3.7 The log functions (p: TBD)

- C17 standard (ISO/IEC 9899:2018):

  - 7.12.6.7 The log functions (p: 178-179)

  - 7.25 Type-generic math <tgmath.h> (p: 272-273)

  - F.10.3.7 The log functions (p: 380)

- C11 standard (ISO/IEC 9899:2011):

  - 7.12.6.7 The log functions (p: 244-245)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - F.10.3.7 The log functions (p: 522)

- C99 standard (ISO/IEC 9899:1999):

  - 7.12.6.7 The log functions (p: 225)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - F.9.3.7 The log functions (p: 459)

- C89/C90 standard (ISO/IEC 9899:1990):

  - 4.5.4.4 The log function

### See also

log10log10flog10l (C99)(C99) | computes common (base-10) logarithm (\({\small \log_{10}{x} }\)log10(x)) (function)
log2log2flog2l (C99)(C99)(C99) | computes base-2 logarithm (\({\small \log_{2}{x} }\)log2(x)) (function)
log1plog1pflog1pl (C99)(C99)(C99) | computes natural (base-e) logarithm of 1 plus the given number (\({\small \ln{(1+x)} }\)ln(1+x)) (function)
expexpfexpl (C99)(C99) | computes e raised to the given power (\({\small e^x}\)ex) (function)
clogclogfclogl (C99)(C99)(C99) | computes the complex natural logarithm (function)
C++ documentation for log

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